Kyrgioz, 19, won the fourth-round tie with Nadal 7-6 (7/5), 5-7, 7-6 (7/5), 6-3 to become the first wildcard in a decade to make the Wimbledon quarterfinals.
Nadal had a disappointing Wimbledon for three years in a row
The teenager also became the first player outside the top 100 to defeat a world number one since Russia's Andrei Olhovskiy shocked Jim Courier in the third round of the Wimbledon 22 years ago.
He is also the first player ranked outside the top 100 to defeat a world number one since Andrei Olhovskiy stunned Jim Courier in the Wimbledon third round in 1992.
For Nadal, who won the title in 2008 and 2010, it was the third successive disappointment. He suffered a first-round exit last year and a second-round loss in 2012.